113 LearnersLast updated on May 30th, 2025
Cube of 108
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used in comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 108.
Cube of 108
A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times.
When you cube a positive number, the result is always positive.
When you cube a negative number, the result is always negative.
This is because a negative number by itself three times results in a negative number.
The cube of 108 can be written as 108³, which is the exponential form.
Or it can also be written in arithmetic form as, 108 × 108 × 108.
How to Calculate the Value of Cube of 108
To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help calculate the cubes faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 108³ = 108 × 108 × 108
Step 2: You get 1,259,712 as the answer. Hence, the cube of 108 is 1,259,712.
Using a Formula (a³)
The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 108 into two parts, as a and b. Let a = 100 and b = 8, so a + b = 108
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 8 3ab² = 3 × 100 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 8)³ = 100³ + 3 × 100² × 8 + 3 × 100 × 8² + 8³ 108³ = 1,000,000 + 240,000 + 19,200 + 512 108³ = 1,259,712
Step 5: Hence, the cube of 108 is 1,259,712.
Using a Calculator
To find the cube of 108 using a calculator, input the number 108 and use the cube function (if available) or multiply 108 × 108 × 108. This operation calculates the value of 108³, resulting in 1,259,712. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 0 and 8
Step 3: If the calculator has a cube function, press it to calculate 108³.
Step 4: If there is no cube function on the calculator, simply multiply 108 three times manually.
Step 5: The calculator will display 1,259,712.
Tips and Tricks for the Cube of 108
- The cube of any even number is always even, while the cube of any odd number is always odd.
- The product of two or more perfect cube numbers is always a perfect cube.
- A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
Common Mistakes to Avoid When Calculating the Cube of 108
There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 108 × 108 and not 108 × 108 × 108. Always remember that 108³ = 108 × 108 × 108.
Solved Examples on Cube of 108
Problem 1
What is the cube and cube root of 108?
The cube of 108 is 1,259,712 and the cube root of 108 is approximately 4.79.
Explanation
First, let’s find the cube of 108. We know that the cube of a number, such that x³ = y
Where x is the given number, and y is the cubed value of that number
So, we get 108³ = 1,259,712
Next, we must find the cube root of 108
We know that the cube root of a number ‘x’, such that ∛x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ∛108 = approximately 4.79
Hence, the cube of 108 is 1,259,712 and the cube root of 108 is approximately 4.79.
Problem 2
If the side length of the cube is 108 cm, what is the volume?
The volume is 1,259,712 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 108 for the side length: V = 108³ = 1,259,712 cm³.
Problem 3
How much larger is 108³ than 100³?
108³ – 100³ = 259,712.
Explanation
First, find the cube of 108³, that is 1,259,712
Next, find the cube of 100³, which is 1,000,000
Now, find the difference between them using the subtraction method. 1,259,712 – 1,000,000 = 259,712
Therefore, 108³ is 259,712 larger than 100³.
Problem 4
If a cube with a side length of 108 cm is compared to a cube with a side length of 8 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 108 cm is 1,259,712 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 108 means multiplying 108 by itself three times: 108 × 108 = 11,664, and then 11,664 × 108 = 1,259,712.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,259,712 cm³.
Problem 5
Estimate the cube of 107.9 using the cube of 108.
The cube of 107.9 is approximately 1,259,712.
Explanation
First, identify the cube of 108,
The cube of 108 is 108³ = 1,259,712.
Since 107.9 is only a tiny bit less than 108, the cube of 107.9 will be almost the same as the cube of 108.
The cube of 107.9 is approximately 1,259,712 because the difference between 107.9 and 108 is very small.
So, we can approximate the value as 1,259,712.
FAQs on Cube of 108
1.What are the perfect cubes up to 108?
2.How do you calculate 108³?
3.What is the meaning of 108³?
4.What is the cube root of 108?
5.Is 108 a perfect cube?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube of 108?
8.How do technology and digital tools in Singapore support learning Algebra and Cube of 108?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube of 108
- Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Cube Root: The number that, when used as a factor three times, gives the original number.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
